We have seen already the normal Chu representation of \(\mathrm {\mathbf {Set}}\)  through \(E^{\mathrm {\mathbf {Set}}, }\)  into \(\textnormal {\textbf {Chu}}(\mathrm {\mathbf {Set}}, )\) .
Next we present the normal Chu representation of the category of Bishop spaces. The notion of Bishop space is a constructive, function-theoretic alternative to the set-based notion of topological space, which was introduced by Bishop in [1]}, revived by Bridges in [2]} and elaborated by the author in [3]}-[4]} and [5]}-[6]}.
For the sake of completeness we give next all necessary definitions related to the proof of a strict Chu representation of the category of Bishop spaces.
